Study on spline wavelet finite-element method in multi-scale analysis for foundation

2013 ◽  
Vol 29 (5) ◽  
pp. 699-708 ◽  
Author(s):  
Qiang Xu ◽  
Jian-Yun Chen ◽  
Jing Li ◽  
Gang Xu ◽  
Hong-Yuan Yue
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Scale Analysis ◽  
Spline Wavelet ◽  
Multi Scale ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Multi Scale Analysis ◽  
Element Method

ADAPTIVE TRIGONOMETRIC HERMITE WAVELET FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350007 ◽  
Author(s):  
WEN-YU HE ◽  
WEI-XIN REN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Element ◽  
Computational Accuracy ◽  
Multi Scale ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Alternative Approach ◽  
Minimum Potential ◽  
Element Method

Owing to its good approximation characteristics of trigonometric functions and the multi-resolution local characteristics of wavelet, the trigonometric Hermite wavelet function is used as the element interpolation function. The corresponding trigonometric wavelet beam element is formulated based on the principle of minimum potential energy. As the order of wavelet can be enhanced easily and the multi-resolution can be achieved by the multi-scale of wavelet, the hierarchical and multi-resolution trigonometric wavelet beam element methods are proposed for the adaptive analysis. Numerical examples have demonstrated that the aforementioned two methods are effective in improving the computational accuracy. The trigonometric wavelet finite element method (WFEM) proposed herein provides an alternative approach for improving the computational accuracy, which can be tailored for the problem considered.

101 On fracture analysis using B-spline wavelet finite element method

2008 ◽  
Vol 2008.46 (0) ◽  
pp. 1-2
Author(s):  
Yuichi SUGIMOTO ◽  
Satoyuki TANAKA ◽  
Hiroshi OKADA ◽  
Masahiko FUJIKUBO ◽  
Shigenobu OKAZAWA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Analysis ◽  
Spline Wavelet ◽  
B Spline ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Element Method

Wavelet Finite Element Method Analysis of Bending Plate Based on Hermite Interpolation

2013 ◽  
Vol 389 ◽  
pp. 267-272 ◽  
Author(s):  
Peng Shen ◽  
Yu Min He ◽  
Zhi Shan Duan ◽  
Zhong Bin Wei ◽  
Pan Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Hermite Interpolation ◽  
Energy Functional ◽  
Field Function ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Crack Problems ◽  
Element Method

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

scholarly journals Wave Motion Analysis in Plane via Hermitian Cubic Spline Wavelet Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaofeng Xue ◽  
Xinhai Wang ◽  
Zhen Wang ◽  
Wei Xue
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Motion Analysis ◽  
Wave Motion ◽  
Shape Functions ◽  
Scale Functions ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Plane Element ◽  
Element Method

A plane Hermitian wavelet finite element method is presented in this paper. Wave motion can be used to analyze plane structures with small defects such as cracks and obtain results. By using the tensor product of modified Hermitian wavelet shape functions, the plane Hermitian wavelet shape functions are constructed. Scale functions of Hermitian wavelet shape functions can replace the polynomial shape functions to construct new wavelet plane elements. As the scale of the shape functions increases, the precision of the new wavelet plane element will be improved. The new Hermitian wavelet finite element method which can be used to simulate wave motion analysis can reveal the law of the wave motion in plane. By using the results of transmitted and reflected wave motion, the cracks can be easily identified in plane. The results show that the new Hermitian plane wavelet finite element method can use the fewer elements to simulate the plane structure effectively and accurately and detect the cracks in plane.

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